Boundary collocation for two dimensional stress analysis of cracks emanating from or from near holes with various shapes

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An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

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Interaction between a circular inclusion and an arbitrarily oriented crack

This paper describes an experimental and theoretical study of the compres sive failure of carbon/epoxy, T800/924C, composite laminates.Static tests were carried out to investigate the mechanics of uniaxial compressive failure in multidirectional unnotched [(±45/02)3]s plates. Fibre microbuckling in the 0° plies is the critical damage mode which causes fracture of the composite plate.A series of experiments was also carried out to determine the failure in compressively loaded [(±45/0 2)3]s laminates with circular holes. X-ray radiography and scanning elec tron microscopy were used to observe damage initiation and propagation. Failure is initi ated as matrix cracking. With increasing load fibre microbuckling, surrounded by delami nation, occurs at the edges of the hole at locations of high in-plane compressive stress. When damage reached a critical state the laminate failed catastrophically.Finally, a theoretical model is presented for predicting the static strength of notched laminates. Theoretical predict...

Static Compression Failure of Carbon Fibre T800/924C Composite Plate with a Single Hole:

The stiffness reduction as a result of multiple transverse cracking in cross-ply laminates and the crack density dependence on the applied tensile stress are analyzed by linear elastic fracture mechanics. The stress field distribution is obtained by the principle of minimum complementary energy. Two models are suggested which describe the non-uniform stress distribution in the thickness direction of the 0° layer. They contain the variational approach presented by Hashin as a particular case. Elastic ply properties and the Mode I critical strain energy release rate GIc for transverse cracking are the experimental data needed. Model predictions are compared with experimental data for glass fiber/epoxy, AS4/3502, and AS/3501-06 carbon fiber/epoxy cross-ply laminates. The predictions from the suggested models describe both the constraint effect and the crack saturation phenomenon.

Multiple Transverse Cracking and Stiffness Reduction in Cross-Ply Laminates

For the 12−node quadrilateral isoparametric elements, it is shown that the inverse square root singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing the quadrilateral elements into triangular elements around the crack tip and placing the two side nodes of each side of the triangles at 1/9 and 4/9 of the length of the side from the tip. This is analogous to placing the mid−side nodes at quarter points in the vicinity of the crack tip for the quadratic isoparametric elements. The advantages of this method are that the displacement compatibility is satisfied throughout the region and that there is no need of special crack tip elements. The stress intensity factors can be accurately obtained by using general purpose programs having isoparametric elements such as NASTRAN.

M. Isida

Papers

On the determination of stress intensity factors for some common structural problems

Analysis of stress intensity factors for the tension of a centrally cracked strip with stiffened edges